The Zero Temperature Phase Diagram of the Kitaev Model

TL;DR

This paper explores the zero temperature phase diagram of the Kitaev model, revealing its correspondence with the classical dimer model and identifying three phases with two transitions, including a novel gapped phase.

Contribution

It establishes a one-to-one correspondence between the Kitaev model's vortex free sector and the classical dimer model, and characterizes the phase transitions.

Findings

Three distinct phases identified in the Kitaev model.

Two phase transitions observed as couplings vary.

Discovery of a new gapped phase within the B phase.

Abstract

We show that the zero temperature phase diagram of the vortex free sector of the Kitaev model is in one to one correspondence with that of the classical dimer model on the same lattice. We find that the model generically has three distinct phases. On a honeycomb lattice with a $3\times3$ fundamental domain all three phases are accessible. As the couplings are varied there are two distinct transitions. The new transition is one to a gapped phase that opens up in the interior of the $B$ phase.